Bond paths as privileged exchange channels

All-body concept and quantified limits of cooperativity and related effects in homodromic cyclic water clusters from a molecular-wide and electron density-based approach

We strongly advocate distinguishing cooperativity from cooperativity-induced effects. From the MOWeD-based approach, the origin of all-body cooperativity is synonymous with physics- and quantum-based processes of electron (e) delocalization throughout water clusters. To this effect, over 10 atom-pairs contribute to the total e-density at a BCP(H,O) between water molecules in a tetramer. Intermolecular all-body e-delocalization, that is, cooperativity, is an energy-minimizing process that fully explains non-additive increase in stability of a water molecule in clusters with an increase in their size. A non-linear change in cooperativity and cooperativity-induced effects, such as (i) structural (e.g., a change in d(O,O)) or topological intra- and intermolecular properties in water clusters (e.g., electron density or potential energy density at bond critical points) is theoretically reproduced by the proposed expression. It predicted the limiting value of delocalized electrons by a H2O molecule in homodromic cyclic clusters to be 1.58e. O-atoms provide the vast majority of electrons that "travel throughout a cluster predominantly on a privileged exchange quantum density highway" (⋅⋅⋅O-H⋅⋅⋅O-H⋅⋅⋅O-H⋅⋅⋅) using Bader's classical bond paths as density bridges linking water molecules. There are, however, additional electron exchange channels that are not seen on molecular graphs as bond paths. A 3D visual representation of the "privileged" and "additional" exchange channels as well as detailed intra- and inter-molecular patterns of e-sharing and (de)localizing is presented. The energy stabilizing contribution made by three O-atoms of neighboring water molecules was found to be large (-597 kcal/mol in cyclic hexamer) and 5 times more significant than that of a classical O-H⋅⋅⋅O intermolecular H-bond.

The Analysis of Electron Densities: From Basics to Emergent Applications

The electron density determines all properties of a system of nuclei and electrons. It is both computable and observable. Its topology allows gaining insight into the mechanisms of bonding and other phenomena in a way that is complementary to and beyond that available from the molecular orbital picture and the formal oxidation state (FOS) formalism. The ability to derive mechanistic insight from electron density is also important with methods where orbitals are not available, such as orbital-free density functional theory (OF-DFT). While density topology-based analyses such as QTAIM (quantum theory of atoms-in-molecules) have been widely used, novel, vector-based techniques recently emerged such as next-generation (NG) QTAIM. Density-dependent quantities are also actively used in machine learning (ML)-based methods, in particular, for ML DFT functional development, including machine-learnt kinetic energy functionals. We review QTAIM and its recent extensions such as NG-QTAIM and localization-delocalization matrices (LDM) and their uses in the analysis of bonding, conformations, mechanisms of redox reactions excitations, as well as ultrafast phenomena. We review recent research showing that direct density analysis can circumvent certain pitfalls of the FOS formalism, in particular in the description of anionic redox, and of the widely used (spherically) projected density of states analysis. We discuss uses of density-based quantities for the construction of DFT functionals and prospects of applications of analyses of density topology to get mechanistic insight with OF-DFT and recently developed time-dependent OF-DFT.

A Dynamical Density Field That Shows the Localizability of Electrons: The Exchange-Correlation Ehrenfest Force

A gradual but steady tide in theoretical chemistry is favoring the exploration of atomic and molecular interactions through the dynamical forces perceived and exerted by the particles of a system. By integrating the quantum mechanical force operator over all the spin and all but one of the spatial coordinates of the electrons, the Ehrenfest force density field reveals these forces directly and is separable into a classical term, related to the electric field, and a quantum mechanical correction, which we introduce and analyze for various atoms and molecules in this work. This exchange-correlation Ehrenfest force density field, Fxc(r), excludes the dominant nuclear components that shape the full Ehrenfest field, revealing information about electron sharing, pairing, and delocalization. In a manner similar, though not equal, to the electron localization function, Fxc(r) unveils covalent and core basins. Its divergence, ∇·Fxc(r), indicates the presence of electron shells in atoms and recovers the positions of lone pairs and the shell structure of ionic, polar, and covalent interactions in molecules. It also exhibits a semiquantitative match with the Laplacian of the electron density that we also explore. In alignment with the established role of exchange-correlation as nature's glue, we demonstrate that a significant number of fundamental concepts in chemical bonding can be derived from the Fxc(r) dynamical field.

A Study of Differential Topology on the Magnetically Induced Isotropically Averaged Lorentz Force Density of a Few Simple Molecules

Quantum chemical topology addresses the study of the chemical structure by applying the tools of differential topology to scalar and vector fields obtained by quantum mechanics. Here, the magnetically induced isotropically averaged Lorentz force density was computed and topologically analyzed for 11 small molecules. Critical points (attractors, repellers, and saddles) were determined and trajectories connecting the attractors computed. It is shown that kinds and numbers of the critical points are to some extent transferable in similar molecules. CC bonds of different orders are endowed with critical points of different kinds close to their center. The sum of topological indices of the isolated critical points is influenced by the presence of repellers on the outer part of the molecules.

Theoretical investigation of benzodithiophene-based donor molecules in organic solar cells: from structural optimization to performance metrics

Achieving high power conversion efficiency (PCE) remains a significant challenge in the advancement of organic solar cells (OSCs). In the field of organic photovoltaics (OPVs), considerable progress has been made in optimizing molecular structures to improve the PCE. However, innovative material design strategies specifically aimed at enhancing PCE are still needed. Here, we have designed BDTS-2DPP-based molecules and propose a molecular design approach to develop donor materials that can significantly improve the PCE of OSCs. Density functional theory (DFT) and time-dependent DFT (TD-DFT) methods have been adopted in both gas and solvent phases. Our newly designed molecule M1 shows the highest absorption value (λ max = 846 nm), highest electron reorganization energy (λ e = 0.18 eV), and the lowest energy gap (E g = 1.81 eV) among all the designed molecules. M1 molecule also exhibits the highest dipole moment in both gas (10.62 D) and solvent phase (13.62 D), and their ground and excited state dipole moment difference is also higher (μ e - μ g = 2.99 D), which enhances its separation to make it a suitable candidate for charge transfer between HOMO-LUMO (97%). Newly designed molecule M3 is observed to have the highest voltage when the current is zero (V oc = 1.15 V) highest PCE value (21.90%) and highest fill factor (FF) value (89.42%). The lowest excitation binding energy is estimated by newly designed molecule M2 (E b = 0.30 eV), which indicates a higher rate of dissociation during the excitation as observed in transition density matrix (TDM) plots. Utilizing electron density difference maps, the newly designed molecules in dichloromethane solvent exhibited consistent intramolecular charge transfer (ICT). The designed molecules were evaluated against reference molecule R to determine if they exhibit superior optoelectronic capabilities. It is found that all designed molecules (M1-M5) exhibit reduced band gaps, are red-shifted in wavelength in comparison to a reference molecule R, and have remarkable charge motilities in terms of reorganisation energies.

Real-space energy decomposition analysis method for qualitative and quantitative interpretations

In the work, a real-space energy decomposition analysis method, called DM-EDA(RS), is introduced based on our recently developed DM-EDA method [Zhang et al., J. Chem. Phys. 160, 174101 (2024)]. The EDA terms in DM-EDA(RS), including electrostatic, exchange, repulsion, polarization, and correlation, are expressed as the summations of grid-based energy density in real-space. This method is able to interpret intermolecular interactions in a unified qualitative and quantitative way. DM-EDA(RS) results provide not only comprehensive explanations for intermolecular interactions but also insights for sub-region interactions involving different functional groups.

New global minimum conformers for the Pt 19 and Pt 20 clusters: low symmetric species featuring different active sites

CONTEXT

The study of platinum (Pt) clusters and nanoparticles is essential due to their extensive range of potential technological applications, particularly in catalysis. The electronic properties that yield optimal catalytic performance at the nanoscale are significantly influenced by the size and structure of Pt clusters. This research aimed to identify the lowest-energy conformers for Pt18 , Pt19 , and Pt20 species using Density Functional Theory (DFT). We discovered new low-symmetry conformers for Pt19 and Pt20 , which are 3.0 and 1.0 kcal/mol more stable, respectively, than previously reported structures. Our study highlights the importance of using density functional approximations that incorporate moderate levels of exact Hartree-Fock exchange, alongside basis sets of at least quadruple-zeta quality. The resulting structures are asymmetric with varying active sites, as evidenced by sigma hole analysis on the electrostatic potential surface. This suggests a potential correlation between electronic structure and catalytic properties, warranting further investigation.

METHODS

An equivariant graph neural network interatomic potential (NequIP) within the Atomic Simulation Environment suite (ASE) was used to provide initial geometries of the aggregates under study. DFT calculations were performed with the ORCA 5 package, using functional approximations that included Generalized Gradient Approximation (PBE), meta-GGA (TPSS, M06-L), hybrid (PBE0, PBEh), meta-GGA hybrid (TPSSh), and range-separated hybrid ( ω B97x) functionals. Def2-TZVP and Def2-QZVP as well as members of the cc-pwCVXZ-PP family to check basis set convergence were used. QTAIM calculations were performed using the AIMAll suite. Structures were visualized with the AVOGADRO code.

Revealing the Critical Role of Global Electron Density Transfer in the Reaction Rate of Polar Organic Reactions within Molecular Electron Density Theory

The critical role of global electron density transfer (GEDT) in increasing the reaction rate of polar organic reactions has been studied within the framework of Molecular Electron Density Theory (MEDT). To this end, the series of the polar Diels-Alder (P-DA) reactions of cyclopentadiene with cyanoethylene derivatives, for which experimental kinetic data are available, have been chosen. A complete linear correlation between the computed activation Gibbs free energies and the GEDT taking place at the polar transition state structures (TSs) is found; the higher the GEDT at the TS, the lower the activation Gibbs free energy. An interacting quantum atoms energy partitioning analysis allows for establishing a complete linear correlation between the electronic stabilization of the electrophilic ethylene frameworks and the GEDT taking place at the polar TSs. This finding supports Parr's proposal for the definition of the electrophilicity ω index. The present MEDT study establishes the critical role of the GEDT in the acceleration of polar reactions, since the electronic stabilization of the electrophilic framework with the electron density gain is greater than the destabilization of the nucleophilic one, making a net favorable electronic contribution to the decrease in the activation energy.

Unusual Ni⋯Ni interaction in Ni(ii) complexes as potential inhibitors for the development of new anti-SARS-CoV-2 Omicron drugs

Two nickel(ii) coordination complexes [Ni(L)]2(1) and [Ni(L)]n(2) of a tetradentate Schiff base ligand (H2L) derived from 2-hydroxy-1-naphthaldehyde with ethylenediamine were synthesized, designed, and characterized via spectroscopic and single crystal XRD analyses. Both nickel(ii) complexes exhibited unusual Ni⋯Ni interactions and were fully characterized via single-crystal X-ray crystallography. Nickel(ii) complexes [Ni(L)]2(1) and [Ni(L)]n(2) crystallize in monoclinic and triclinic crystal systems with P21/c and P1̄ space groups, respectively, and revealed square planar geometry around each Ni(ii) ion. The structure of both the complexes have established the existence of a new kind of metal system containing nickel(ii)-nickel(ii) interactions with a square planar-like geometry about the nickel(ii) atoms. Both square planar Ni(ii) complexes were often stacked with relatively short Ni⋯Ni distances. The non-bonded Ni-Ni distance (Ni⋯Ni separation) seems to be 3.356 Å and 3.214 Å from the nickel atoms of [Ni(L)]2(1) and [Ni(L)]n(2), respectively. These distances are shorter than the sum of their van der Waals radii (4.80 Å) but longer than the sum of their covalent radii (2.50 Å), indicating that there is a Ni⋯Ni interaction but not a Ni-Ni bond. The discrete molecules are π-stacked and connected via weak intermolecular interactions (C-H⋯O and C-H⋯N). Cyclic voltammetry measurements were obtained for both the complexes, and their pharmacokinetic and chemoinformatics properties were also explored. Detailed structural analysis and non-covalent supramolecular interactions were investigated using single-crystal structure analysis and computational approaches. Both the unique structures show good inhibition performance for the Omicron spike proteins of the SARS CoV-2 virus. To gain insights into potential SARS-CoV-2 Omicron drugs and find inhibitors against the Omicron variants of SARS-CoV-2, we examined the molecular docking of the nickel(ii) complexes [Ni(L)]2(1) and [Ni(L)]n(2) with the SARS-CoV-2 Omicron spike protein (PDB ID: 7WK2 and 7WVO). A strong binding was predicted between Ni(ii) coordination complexes [Ni(L)]2(1) and [Ni(L)]n(2) with the SARS-CoV-2 Omicron variant receptor protein through the negative value of binding affinity. Molecular docking of Nil(ii) complexes [Ni(L)]2(1) and [Ni(L)]n(2) with a DNA duplex (PDB ID: 7D3T) and RNA (PDB ID: 7TDC) binding protein was also studied. Overall, this study suggests that Ni(ii) complexes can be considered as drug candidates against the Omicron variants of SARS-CoV-2.

Probing Non-Covalent Interactions through Molecular Balances: A REG-IQA Study

The interaction energies of two series of molecular balances (1-X with X = H, Me, OMe, NMe2 and 2-Y with Y = H, CN, NO2, OMe, NMe2) designed to probe carbonyl…carbonyl interactions were analysed at the B3LYP/6-311++G(d,p)-D3 level of theory using the energy partitioning method of Interacting Quantum Atoms/Fragments (IQA/IQF). The partitioned energies are analysed by the Relative Energy Gradient (REG) method, which calculates the correlation between these energies and the total energy of a system, thereby explaining the role atoms have in the energetic behaviour of the total system. The traditional "back-of-the-envelope" open and closed conformations of molecular balances do not correspond to those of the lowest energy. Hence, more care needs to be taken when considering which geometries to use for comparison with the experiment. The REG-IQA method shows that the 1-H and 1-OMe balances behave differently to the 1-Me and 1-NMe2 balances because the latter show more prominent electrostatics between carbonyl groups and undergoes a larger dihedral rotation due to the bulkiness of the functional groups. For the 2-Y balance, REG-IQA shows the same behaviour across the series as the 1-H and 1-OMe balances. From an atomistic point of view, the formation of the closed conformer is favoured by polarisation and charge-transfer effects on the amide bond across all balances and is counterbalanced by a de-pyramidalisation of the amide nitrogen. Moreover, focusing on the oxygen of the amide carbonyl and the α-carbon of the remaining carbonyl group, electrostatics have a major role in the formation of the closed conformer, which goes against the well-known n-π* interaction orbital overlap concept. However, REG-IQF shows that exchange-correlation energies overtake electrostatics for all the 2-Y balances when working with fragments around the carbonyl groups, while they act on par with electrostatics for the 1-OMe and 1-NMe2. REG-IQF also shows that exchange-correlation energies in the 2-Y balance are correlated to the inductive electron-donating and -withdrawing trends on aromatic groups. We demonstrate that methods such as REG-IQA/IQF can help with the fine-tuning of molecular balances prior to the experiment and that the energies that govern the probed interactions are highly dependent on the atoms and functional groups involved.

The Ehrenfest force field: A perspective based on electron density functions

The topology of the Ehrenfest force field (EhF) is investigated as a tool for describing local interactions in molecules and intermolecular complexes. The EhF is obtained by integrating the electronic force operator over the coordinates of all but one electron, which requires knowledge of both the electron density and the reduced pair density. For stationary states, the EhF can also be obtained as minus the divergence of the kinetic stress tensor, although this approach leads to well-documented erroneous asymptotic behavior at large distances from the nuclei. It is shown that these pathologies disappear using the electron density functions and that the EhF thus obtained displays the correct behavior in real space, with no spurious critical points or attractors. Therefore, its critical points can be unambiguously obtained and classified. Test cases, including strained molecules, isomerization reactions, and intermolecular interactions, were analyzed. Various chemically relevant facts are highlighted: for example, non-nuclear attractors are generally absent, potential hydrogen-hydrogen interactions are detected in crowded systems, and a bifurcation mechanism is observed in the isomerization of HCN. Moreover, the EhF atomic basins are less charged than those of the electron density. Although integration of the EhF over regions of real space can also be performed to yield the corresponding atomic forces, several numerical drawbacks still need to be solved if electron density functions are to be used for that purpose. Overall, the results obtained support the Ehrenfest force field as a reliable descriptor for the definition of atomic basins and molecular structure.

Electron density-based protocol to recover the interacting quantum atoms components of intermolecular binding energy

A new approach for obtaining interacting quantum atoms-defined components of binding energy of intermolecular interactions, which bypasses the use of standard six-dimensional integrals and two-particle reduced density matrix (2-RDM) reconstruction, is proposed. To examine this approach, three datasets calculated within the density functional theory framework using the def2-TZVP basis have been explored. The first two, containing 53 weakly bound bimolecular associates and 13 molecular clusters taken from the crystal, were used in protocol refinement, and the third one containing other 20 bimolecular and three cluster systems served as a validation reference. In addition, to verify the performance of the proposed approach on an exact 2-RDM, calculations within the coupled cluster formalism were performed for part of the first set systems using the cc-pVTZ basis set. The process of optimization of the proposed parametric model is considered, and the role of various energy contributions in the formation of non-covalent interactions is discussed with regard to the obtained trends.

Interacting Quantum Atoms and Multipolar Electrostatic Study of XH···π Interactions

The interaction energies of nine XH···π (X = C, N, and O) benzene-containing van der Waals complexes were analyzed, at the atomic and fragment levels, using QTAIM multipolar electrostatics and the energy partitioning method interacting quantum atoms/fragment (IQA/IQF). These descriptors were paired with the relative energy gradient method, which solidifies the connection between quantum mechanical properties and chemical interpretation. This combination provides a precise understanding, both qualitative and quantitative, of the nature of these interactions, which are ubiquitous in biochemical systems. The formation of the OH···π and NH···π systems is electrostatically driven, with the Qzz component of the quadrupole moment of the benzene carbons interacting with the charges of X and H in XH. There is the unexpectedly intramonomeric role of X-H (X = O, N) where its electrostatic energy helps the formation of the complex and its covalent energy thwarts it. However, the CH···π interaction is governed by exchange-correlation energies, thereby establishing a covalent character, as opposed to the literature's designation as a noncovalent interaction. Moreover, dispersion energy is relevant, statically and in absolute terms, but less relevant compared to other energy components in terms of the formation of the complex. Multipolar electrostatics are similar across all systems.

New Boron Containing Acridines: Synthesis and Preliminary Biological Study

The synthesis of the first conjugates of acridine with cobalt bis(dicarbollide) are reported. A novel 9-azido derivative of acridine was prepared through the reaction of 9-methoxyacridine with N3CH2CH2NH2, and its solid-state molecular structure was determined via single-crystal X-ray diffraction. The azidoacridine was used in a copper (I)-catalyzed azide-alkyne cycloaddition reaction with cobalt bis(dicarbollide)-based terminal alkynes to give the target 1,2,3-triazoles. DNA interaction studies via absorbance spectroscopy showed the weak binding of the obtained conjugates with DNA. The antiproliferative activity (IC50) of the boronated conjugates against a series of human cell lines was evaluated through an MTT assay. The results suggested that acridine derivatives of cobalt bis(dicarbollide) might serve as a novel scaffold for the future development of new agents for boron neutron capture therapy (BNCT).

A Molecular Electron Density Theory Study of the Domino Reaction of N-Phenyl Iminoboranes with Benzaldehyde Yielding Fused Bicyclic Compounds

The reaction of N-phenyl iminoborane with benzaldehyde yielding a fused aromatic compound, recently reported by Liu et al., has been studied within the Molecular Electron Density Theory (MEDT). Formation of the fused aromatic compound is a domino process that comprises three consecutive reactions: (i) formation of a weak molecular complex between the reagents; (ii) an intramolecular electrophilic attack of the activated carbonyl carbon of benzaldehyde on the ortho position of the N-phenyl substituent of iminoborane; and (iii) a formal 1,3-hydrogen shift yielding the final fused aromatic compound. The two last steps correspond to a Friedel-Crafts acylation reaction, the product of the second reaction being the tetrahedral intermediate of an electrophilic aromatic substitution reaction. However, the presence of the imino group adjacent to the aromatic ring strongly stabilizes the corresponding intermediate, being the reaction product when the ortho positions are occupied by t-butyl substituents. This domino reaction shows a great similitude with the Brønsted acid catalyzed Povarov reaction. Although N-phenyl iminoborane can experience a formal [2+2] cycloaddition reaction with benzaldehyde, its higher activation Gibbs free energy compared to the intramolecular electrophilic attack of the activated carbonyl carbon of benzaldehyde on the ortho position of the N-phenyl substituent, 6.6 kcal·mol-1, prevents the formation of the formal [2+2] cycloadduct. The present MEDT study provides a different vision of the molecular mechanism of these reactions based on the electron density.

How to Compute Atomistic Insight in DFT Clusters: The REG-IQA Approach

The relative energy gradient (REG) method is paired with the topological energy partitioning method interacting quantum atoms (IQA), as REG-IQA, to provide detailed and unbiased knowledge on the intra- and interatomic interactions. REG operates on a sequence of geometries representing a dynamical change of a system. Its recent application to peptide hydrolysis of the human immunodeficiency virus-1 (HIV-1) protease (PDB code: 4HVP) has demonstrated its full potential in recovering reaction mechanisms and through-space electrostatic and exchange-correlation effects, making it a compelling tool for analyzing enzymatic reactions. In this study, the computational efficiency of the REG-IQA method for the 133-atom HIV-1 protease quantum mechanical system is analyzed in every detail and substantially improved by means of three different approaches. The first approach of smaller integration grids for IQA integrations reduces the computational overhead by about a factor of 3. The second approach uses the line-simplification Ramer-Douglas-Peucker (RDP) algorithm, which outputs the minimal number of geometries necessary for the REG-IQA analysis for a predetermined root mean squared error (RMSE) tolerance. This cuts the computational time of the whole REG analysis by a factor of 2 if an RMSE of 0.5 kJ/mol is considered. The third approach consists of a "biased" or "unbiased" selection of a specific subset of atoms of the whole initial quantum mechanical model wave-function, which results in more than a 10-fold speed-up per geometry for the IQA calculation, without deterioration of the outcome of the REG-IQA analysis. Finally, to show the capability of these approaches, the findings gathered from the HIV-1 protease system are also applied to a different system named haloalcohol dehalogenase (HheC). In summary, this study takes the REG-IQA method to a computationally feasible and highly accurate level, making it viable for the analysis of a multitude of enzymatic systems.

Nature and Strength of Weak O⋅⋅⋅O Interactions in Nitryl Halide Dimers

The use of real space functions and molecular graphs has pushed some chemists to wonder: Are interactions between negatively charged oxygen atoms possible? In this contribution we analyze whether there is a real interaction between oxygen atoms in nitryl halide dimers (XNO₂ )₂ (X=F, Cl, Br and I) and in tetranitromethane and derivatives. Based on ab-initio and density functional theories (DFT) methods, we show these complexes are weakly stabilized. Energy decomposition analyses based on local molecular orbitals (LMOEDA) and interacting quantum atoms (IQA) reveal both dispersion and exchange play a crucial role in the stabilization of these complexes. Electron charge density and IQA analyses indicate that the oxygen atoms are connected by privileged exchange channels. In addition, electrostatic interactions between O and N atoms are also vital for the stabilization of the complexes. Finally, a reasonable explanation is given for the dynamic behavior of nitryl groups in tetranitromethane and derivatives.

Real-Space Interpretation of Interatomic Charge Transfer and Electron Exchange Effects by Combining Static and Kinetic Potentials and Associated Vector Fields

Intricate behaviour of one-electron potentials from the Euler equation for electron density and corresponding gradient force fields in crystals was studied. Channels of locally enhanced kinetic potential and corresponding saddle Lagrange points were found between chemically bonded atoms. Superposition of electrostatic ϕ e s r and kinetic ϕ k r potentials and electron density ρ r allowed partitioning any molecules and crystals into atomic ρ - and potential-based ϕ -basins; ϕ k -basins explicitly account for the electron exchange effect, which is missed for ϕ e s -ones. Phenomena of interatomic charge transfer and related electron exchange were explained in terms of space gaps between zero-flux surfaces of ρ - and ϕ -basins. The gap between ϕ e s - and ρ -basins represents the charge transfer, while the gap between ϕ k - and ρ -basins is a real-space manifestation of sharing the transferred electrons caused by the static exchange and kinetic effects as a response against the electron transfer. The regularity describing relative positions of ρ -, ϕ e s -, and ϕ k - basin boundaries between interacting atoms was proposed. The position of ϕ k -boundary between ϕ e s - and ρ -ones within an electron occupier atom determines the extent of transferred electron sharing. The stronger an H⋅⋅⋅O hydrogen bond is, the deeper hydrogen atom's ϕ k -basin penetrates oxygen atom's ρ -basin, while for covalent bonds a ϕ k -boundary closely approaches a ϕ e s -one indicating almost complete sharing of the transferred electrons. In the case of ionic bonds, the same region corresponds to electron pairing within the ρ -basin of an electron occupier atom.

Non-covalent interactions from a Quantum Chemical Topology perspective

About half a century after its little-known beginnings, the quantum topological approach called QTAIM has grown into a widespread, but still not mainstream, methodology of interpretational quantum chemistry. Although often confused in textbooks with yet another population analysis, be it perhaps an elegant but somewhat esoteric one, QTAIM has been enriched with about a dozen other research areas sharing its main mathematical language, such as Interacting Quantum Atoms (IQA) or Electron Localisation Function (ELF), to form an overarching approach called Quantum Chemical Topology (QCT). Instead of reviewing the latter's role in understanding non-covalent interactions, we propose a number of ideas emerging from the full consequences of the space-filling nature of topological atoms, and discuss how they (will) impact on interatomic interactions, including non-covalent ones. The architecture of a force field called FFLUX, which is based on these ideas, is outlined. A new method called Relative Energy Gradient (REG) is put forward, which is able, by computation, to detect which fragments of a given molecular assembly govern the energetic behaviour of this whole assembly. This method can offer insight into the typical balance of competing atomic energies both in covalent and non-covalent case studies. A brief discussion on so-called bond critical points is given, highlighting concerns about their meaning, mainly in the arena of non-covalent interactions.

Electronegativity Equilibration

Controlling the distribution of electrons in materials is the holy grail of chemistry and material science. Practical attempts at this feat are common but are often reliant on simplistic arguments based on electronegativity. One challenge is knowing when such arguments work, and which other factors may play a role. Ultimately, electrons move to equalize chemical potentials. In this work, we outline a theory in which chemical potentials of atoms and molecules are expressed in terms of reinterpretations of common chemical concepts and some physical quantities: electronegativity, chemical hardness, and the sensitivity of electronic repulsion and core levels with respect to changes in the electron density. At the zero-temperature limit, an expression of the Fermi level emerges that helps to connect several of these quantities to a plethora of material properties, theories and phenomena predominantly explored in condensed matter physics. Our theory runs counter to Sanderson's postulate of electronegativity equalization and allows a perspective in which electronegativities of bonded atoms need not be equal. As chemical potentials equalize in this framework, electronegativities equilibrate.

Synthesis and Structure Elucidation of Novel Spirooxindole Linked to Ferrocene and Triazole Systems via [3 + 2] Cycloaddition Reaction

In the present work, a novel heterocyclic hybrid of a spirooxindole system was synthesized via the attachment of ferrocene and triazole motifs into an azomethine ylide by [3 + 2] cycloaddition reaction protocol. The X-ray structure of the heterocyclic hybrid (1″R,2″S,3R)-2″-(1-(3-chloro-4-fluorophenyl)-5-methyl-1H-1,2,3-triazole-4-carbonyl)-5-methyl-1″-(ferrocin-2-yl)-1″,2″,5″,6″,7″,7a″-hexahydrospiro[indoline-3,3″-pyrrolizin]-2-one revealed very well the expected structure, by using different analytical tools (FTIR and NMR spectroscopy). It crystallized in the triclinic-crystal system and the P-1-space group. The unit cell parameters are a = 9.1442(2) Å, b = 12.0872(3) Å, c = 14.1223(4) Å, α = 102.1700(10)°, β = 97.4190(10)°, γ = 99.1600(10)°, and V = 1484.81(7) ų. There are two molecules per unit cell and one formula unit per asymmetric unit. Hirshfeld analysis was used to study the molecular packing of the heterocyclic hybrid. H···H (50.8%), H···C (14.2%), Cl···H (8.9%), O···H (7.3%), and N···H (5.1%) are the most dominant intermolecular contacts in the crystal structure. O···H, N···H, H···C, F···H, F···C, and O···O are the only contacts that have the characteristic features of short and significant interactions. AIM study indicated predominant covalent characters for the Fe–C interactions. Also, the electron density (ρ(r)) at the bond critical point correlated inversely with the Fe–C distances.

Finding critical points and reconstruction of electron densities on grids

The quantum theory of atoms in molecules (QTAIM), developed by Bader and co-workers, is one of the most popular ways of extracting chemical insight from the results of quantum mechanical calculations. One of the basic tasks in QTAIM is to locate the critical points of the electron density and calculate various quantities (density, Laplacian, etc.) on them since these have been found to correlate with molecular properties of interest. If the electron density is given analytically, this process is relatively straightforward. However, locating the critical points is more challenging if the density is known only on a three-dimensional uniform grid. A density grid is common in periodic solids because it is the natural expression for the electron density in plane-wave calculations. In this article, we explore the reconstruction of the electron density from a grid and its use in critical point localization. The proposed reconstruction method employs polyharmonic spline interpolation combined with a smoothing function based on the promolecular density. The critical point search based on this reconstruction is accurate, trivially parallelizable, works for periodic and non-periodic systems, does not present directional lattice bias when the grid is non-orthogonal, and locates all critical points of the underlying electron density in all tests studied. The proposed method also provides an accurate reconstruction of the electron density over the space spanned by the grid, which may be useful in other contexts besides critical point localization.

Synthesis, X-ray, Hirshfeld, and AIM Studies on Zn(II) and Cd(II) Complexes with Pyridine Ligands

The synthesis and crystal structures of three heteroleptic complexes of Zn(II) and Cd(II) with pyridine ligands (ethyl nicotinate (EtNic), N,N-diethylnicotinamide (DiEtNA), and 2-amino-5-picoline (2Ampic) are presented. The complex [Zn(EtNic)2Cl2] (1) showed a distorted tetrahedral coordination geometry with two EtNic ligand units and two chloride ions as monodentate ligands. Complexes [Zn(DiEtNA)(H2O)4(SO4)]·H2O (2) and [Cd(OAc)2(2Ampic)2] (3) had hexa-coordinated Zn(II) and Cd(II) centers. In the former, the Zn(II) was coordinated with three different monodentate ligands, which were DiEtNA, H2O, and SO42−. In 3, the Cd(II) ion was coordinated with two bidentate acetate ions and two monodentate 2Ampic ligand units. The supramolecular structures of the three complexes were elucidated using Hirshfeld analysis. In 1, the most important interactions that governed the molecular packing were O···H (15.5–15.6%), Cl···H (13.6–13.8%), Cl···C (6.3%), and C···H (10.3–10.6%) contacts. For complexes 2 and 3, the H···H, O···H, and C···H contacts dominated. Their percentages were 50.2%, 41.2%, and 7.1%, respectively, for 2 and 57.1%, 19.6%, and 15.2%, respectively, for 3. Only in complex 3, weak π-π stacking interactions between the stacked pyridines were found. The Zn(II) natural charges were calculated using the DFT method to be 0.8775, 1.0559, and 1.2193 for complexes 1–3, respectively. A predominant closed-shell character for the Zn–Cl, Zn–N, Zn–O, Cd–O, and Cd–N bonds was also concluded from an atoms in molecules (AIM) study.

Intrinsic Dynamic and Static Nature of π···π Interactions in Fused Benzene-Type Helicenes and Dimers, Elucidated with QTAIM Dual Functional Analysis

The intrinsic dynamic and static nature of the π···π interactions between the phenyl groups in proximity of helicenes 3-12 are elucidated with the quantum theory of atoms-in-molecules dual functional analysis (QTAIM-DFA). The π···π interactions appear in C-∗-C, H-∗-H, and C-∗-H, with the asterisks indicating the existence of bond critical points (BCPs) on the interactions. The interactions of 3-12 are all predicted to have a p-CS/vdW nature (vdW nature of the pure closed-shell interaction), except for 2Cbay-∗-7Cbay of 10, which has a p-CS/t-HBnc nature (typical-HBs with no covalency). (See the text for definition of the numbers of C and the bay and cape areas). The natures of the interactions are similarly elucidated between the components of helicene dimers 6:6 and 7:7 with QTAIM-DFA, which have a p-CS/vdW nature. The characteristic electronic structures of helicenes are clarified through the natures predicted with QTAIM-DFA. Some bond paths (BPs) in helicenes appeared or disappeared, depending on the calculation methods. The static nature of Ccape-∗-Ccape is very similar to that of Cbay-∗-Cbay in 9-12, whereas the dynamic nature of Ccape-∗-Ccape appears to be very different from that of Cbay-∗-Cbay. The results will be a guide to design the helicene-containing materials of high functionality.

Control of Molecular Conformation and Crystal Packing of Biphenyl Derivatives

This Review presents a discussion of the conformation of biphenyl derivatives in different chemical environments. The interplay between aromatic stabilization and steric repulsion, normally considered to explain the conformation of the molecule, is contrasted with the interpretation provided by models not based on molecular orbitals. The electronic control of conformation by means of appropriate hydrogen substitution is discussed by examples taken from chemistry and molecular electronics. Supramolecular synthons involving biphenyl are critically analyzed in terms of the molecular conformation, crystal packing and intermolecular forces. Some directions for future research on the control of the conformation of biphenyls are also presented.

Long-range supramolecular synthon polymorphism: a case study of two new polymorphic cocrystals of Ph2Te2–1,4-C6F4I2

Two new polymorphic forms of Ph2Te2–1,4-C6F4I2 cocrystals feature an unusual packing of Ph2Te2 molecules, which is typical for native Ph2Se2 but not Ph2Te2. This suggests the existence the yet unknown, Ph2Se2-like polymorph of Ph2Te2.

Nucleophilic addition reactions to nitrilium derivatives [B12H11NCCH3]- and [B12H11NCCH2CH3]-. Synthesis and structure of closo-dodecaborate-based iminols, amides and amidines

The synthesis of the acetonitrilium and propioitrilium derivatives of closo-dodecaborate [B12H12]2- were discussed. The nucleophilic addition reactions of water, alcohols and secondary amines to the activated triple bond of the...

Molecular, Supramolecular Structures Combined with Hirshfeld and DFT Studies of Centrosymmetric M(II)-azido {M=Ni(II), Fe(II) or Zn(II)} Complexes of 4-Benzoylpyridine

The supramolecular structures of the three metal (II) azido complexes [Fe(4bzpy)4(N3)2]; 1, [Ni(4bzpy)4(N3)2]; 2 and [Zn(4bzpy)2(N3)2]n; 3 with 4-benzoylpyridine (4bzpy) were presented. All complexes contain hexa-coordinated divalent metal ions with a slightly distorted octahedral MN6 coordination sphere. Complexes 1 and 2 are monomeric with terminal azido groups while 3 is one-dimensional coordination polymer containing azido groups with μ(1,1) and μ(1,3) bridging modes of bonding. Hirshfeld analysis was used to quantitatively determine the different contacts affecting the molecular packing in the studied complexes. The most common interactions are the polar O…H and N…H interactions and the hydrophobic C…H contacts. The charges at the M(II) sites are calculated to be 1.004, 0.847, and 1.147 e for complexes 1–3, respectively. The degree of asymmetry is the highest in the case of the terminal azide in complexes 1 and 2 while was found the lowest in the μ(1,1) and μ(1,3) azide bonding modes in the Zn(II) complex 3. These facts were further explained in terms of atoms in molecules (AIM) topological parameters.

Acenes and phenacenes in their lowest-lying triplet states. Does kinked remain more stable than straight?

The larger stability of phenacenes compared to their acene isomers in their ground states is attributed to the larger aromaticity of the former. To our knowledge the relative stability of acenes and phenacenes in their lowest-lying triplet states (T1) has not been discussed yet. Using unrestricted density functional theory calculations, our results show that for the smallest members of the series, acenes in their T1 states are more stable than the corresponding phenacenes. However, when the number of the rings (n) involved increases, the energy difference is reduced and for n > 12, phenacenes become more stable than acenes in their T1 states. To rationalize this trend, we analyze the aromaticity of acenes and phenacenes using a set of aromaticity descriptors. We find that in the T1 states of both acenes and phenacenes, the outer rings form aromatic Clar π-sextets. In acenes, delocalization of spin density in the central rings leads to the preferred formation of the largest antiaromatic diradical. Resonant structures in the form of antiaromatic diradical Baird π-octadectets and π-tetradectets are the major contributors, while the smaller ones, such as π-doublets and π-sextets, contribute the least. In phenacenes, structures with diradical antiaromatic Baird π-sextets in some of the central rings contribute the most. These results are relevant to understand the (anti)aromaticity of larger polycyclic aromatic hydrocarbons in their triplet states.

Electrostatic Potential Topology for Probing Molecular Structure, Bonding and Reactivity

Following the pioneering investigations of Bader on the topology of molecular electron density, the topology analysis of its sister field viz. molecular electrostatic potential (MESP) was taken up by the authors’ groups. Through these studies, MESP topology emerged as a powerful tool for exploring molecular bonding and reactivity patterns. The MESP topology features are mapped in terms of its critical points (CPs), such as bond critical points (BCPs), while the minima identify electron-rich locations, such as lone pairs and π-bonds. The gradient paths of MESP vividly bring out the atoms-in-molecule picture of neutral molecules and anions. The MESP-based characterization of a molecule in terms of electron-rich and -deficient regions provides a robust prediction about its interaction with other molecules. This leads to a clear picture of molecular aggregation, hydrogen bonding, lone pair–π interactions, π-conjugation, aromaticity and reaction mechanisms. This review summarizes the contributions of the authors’ groups over the last three decades and those of the other active groups towards understanding chemical bonding, molecular recognition, and reactivity through topology analysis of MESP.

The CH···HC interaction in biphenyl is a delocalized, molecular-wide and entirely non-classical interaction: Results from FALDI analysis

In this study we aim to determine the origin of the electron density describing a CH···HC interaction in planar and twisted conformers of biphenyl. In order to achieve this, the fragment, atomic, localized, delocalized, intra- and inter-atomic (FALDI) decomposition scheme was utilized to decompose the density in the inter-nuclear region between the ortho-hydrogens in both conformers. Importantly, the structural integrity, hence also topological properties, were fully preserved as no 'artificial' partitioning of molecules was implemented. FALDI-based qualitative and quantitative analysis revealed that the majority of electron density arises from two, non-classical and non-local effects: strong overlap of ortho CH σ-bonds, and long-range electron delocalization between the phenyl rings and ortho carbons and hydrogens. These effects resulted in a delocalized electron channel, that is, a density bridge or a bond path in a QTAIM terminology, linking the H-atoms in the planar conformer. The same effects and phenomena are present in both conformers of biphenyl. We show that the CH···HC interaction is a molecular-wide event due to large and long-range electron delocalization, and caution against approaches that investigate CH···HC interactions without fully taking into account the remainder of the molecule.

Synthesis and Structure of Nido-Carboranyl Azide and Its "Click" Reactions

Novel zwitter-ionic nido-carboranyl azide 9-N3(CH2)3Me2N-nido-7,8-C2B9H11 was prepared by the reaction of 9-Cl(CH2)3Me2N-nido-7,8-C2B9H11 with NaN3. The solid-state molecular structure of nido-carboranyl azide was determined by single-crystal X-ray diffraction. 9-N3(CH2)3Me2N-nido-7,8-C2B9H11 was used for the copper(I)-catalyzed azide-alkyne cycloaddition with phenylacetylene, alkynyl-3β-cholesterol and cobalt/iron bis(dicarbollide) terminal alkynes to form the target 1,2,3-triazoles. The nido-carborane-cholesterol conjugate 9-3β-Chol-O(CH2)C-CH-N3(CH2)3Me2N-nido-7,8-C2B9H11 with charge-compensated group in a linker can be used as a precursor for preparation of liposomes for Boron Neutron Capture Therapy (BNCT). A series of novel zwitter-ionic boron-enriched cluster compounds bearing a 1,2,3-triazol-metallacarborane-carborane conjugated system was synthesized. Prepared conjugates contain a large amount of boron atom in the biomolecule and potentially can be used for BNCT.

Predicted structure and selectivity of 3d transition metal complexes with glutamic N,N-bis(carboxymethyl) acid

Structure and selectivity of 3d transition metal complexes with glutamic N,N-bis(carboxymethyl) acid are analyzed and predicted from DFT calculations.

A Critical Overview of Current Theoretical Methods of Estimating the Energy of Intramolecular Interactions

This article is probably the first such comprehensive review of theoretical methods for estimating the energy of intramolecular hydrogen bonds or other interactions that are frequently the subject of scientific research. Rather than on a plethora of numerical data, the main focus is on discussing the theoretical rationale of each method. Additionally, attention is paid to the fact that it is very often possible to use several variants of a particular method. Both of the methods themselves and their variants often give wide ranges of the obtained estimates. Attention is drawn to the fact that the applicability of a particular method may be significantly limited by various factors that disturb the reliability of the estimation, such as considerable structural changes or new important interactions in the reference system.

A Sterically Hindered Derivative of 2,1,3-Benzotelluradiazole: A Way to the First Structurally Characterised Monomeric Tellurium-Nitrogen Radical Anion

Interaction of the tetradentate redox-active 6,6'-[1,2-phenylenebis(azanediyl)]bis(2,4-di-tert-butylphenol) (H₄ L) with TeCl₄ leads to neutral diamagnetic compound TeL (1) in high yield. The molecule of 1 has a nearly planar TeN₂ O₂ fragment, which suggests the formulation of 1 as Te^II L^2- , in agreement with the results of DFT calculations and QTAIM and NBO analyses. Reduction of 1 with one equivalent of [CoCp₂ ] leads to quantitative formation of the paramagnetic salt [CoCp₂ ]⁺ [1]^.- , which was characterised by single-crystal XRD. The solution EPR spectrum of [CoCp₂ ]⁺ [1]^.- at room temperature features a quintet due to splitting on two equivalent ¹⁴ N nuclei. Below 150 K it turns into a broad singlet line with two weak satellites due to the splitting on the ¹²⁵ Te nucleus. Two-component relativistic DFT calculations perfectly reproduce the a(¹⁴ N) HFI constants and A_∥ (¹²⁵ Te) value responsible for the low-temperature satellite splitting. Calculations predict that the additional electron in 1^.- is localised mainly on L, while the spin density is delocalised over the whole molecule with significant localisation on the Te atom (≥30 %). All these data suggest that 1^.- can be regarded as the first example of a structurally characterised monomeric tellurium-nitrogen radical anion.

Cooperativity in a cycloalkane-1,2/1,3-polyol corona: Topological hydrogen bonding in 1,2-diol motifs

A corona, consisting of 18 carbon atoms bearing 12 hydroxy groups in a continuous hydrogen-bonded chain, is built up by alternating degenerate conformations of alternating alkane-1,2-diol and 1,3-diol motifs. Geometries, proton nuclear magnetic resonance shifts and interaction energies for the dodecahydroxycyclo-octadecane and selected fragments are determined by density functional calculations at the B3LYP/6-311+G(d,p) level. Cooperative effects of O-H⋯O-H bonding are evident from the simple juxtaposition of these two motifs with a common OH group in butane-1,2,4-triol conformers. Bracketing a 1,2-diol motif with two 1,3-diol motifs in hexane-1,3,4,6-tetrol leads to a structure in which the 1,2-diol motif displays a bond critical point for hydrogen bonding. This is associated with enhancement of the shift of the hydrogen-bonded OH proton and of the corresponding H⋯O interaction energy. The full corona has a complete outer ring of O-H⋯O-H bond paths, and an inner ring of bond paths, due to C-H⋯H-C hydrogen-hydrogen bonding, which result in a central ring critical point. The topological O-H⋯O-H hydrogen bond, never seen in simple alkane-1,2-diols, is associated with cooperative enhancement of the H⋯O interaction energy, but this is not a necessary condition for a bond path: values for topological C-H⋯H-C hydrogen-hydrogen bonds can be as low as -0.4 kcal mol^-1 .

Looking at local classical and quantum forces in stable crystals using multipole-model refined electron densities and orbital-free DFT approximations

Two distinct approaches, that of energy and that of force, are adopted in quantum mechanics to get insights on chemical processes. In the second one, the net forces acting on the electrons and nuclei in a system (Ehrnefest and Hellmann-Feynman forces, respectively) are determined and a local version of the approach, in terms of force density fields rather than forces, has also been proposed for electrons. This is the path followed by Tsirelson & Stash (2020) in this issue of Acta Crystallographica Section B, to study for the first time the spatial distribution of the electronic forces of different nature acting in stable crystals. Interestingly, by relying on approximations taken from orbital-free DFT, all components of the inner-crystal force can be easily retrieved from multipole-model refined experimental electron densities and their derivatives. No less important is that these calculations are becoming easily doable for any X-ray density crystallographer thanks to a new version of the computer program WinXPRO, purposely developed in the study which is discussed in this commentary.

Steric clash in real space: biphenyl revisited

A textbook case of twisted structure due to hydrogen-hydrogen steric clash, the biphenyl molecule, has been studied in real space from a new perspective. Long-term discrepancies regarding the origin of the steric repulsion are now reconciled under the NCI (Non Covalent Interaction) method, which reflects in 3D the balance between attractive and repulsive interactions taking place in the region between the phenyl rings. The NCI method confirms that the steric repulsion does not merely come from the H-H interaction itself, but from the many-atom interactions arising from the Cortho-H region, therefore providing rigorous physical grounds for the steric clash. This method allows a continuous scan of all the subtle changes on the electron density on going from the planar to the perpendicular biphenyl structure. The NCI results agree with other topological approaches (IQA, ELF) and are in line with previous findings in the literature regarding controversial H-H interactions in steric clash situations: H-H interactions are attractive, but repulsion appears between (Cortho-H)(Cortho-H), raising the intraatomic energy of the ortho H. ELF is also used to support these conclusions. Indeed, deformations are observed in compressed basins that allow to visualize the intraatomic effect of steric repulsion. These results can be easily extrapolated to systems with similar topological features in which steric clash is claimed to be the reason for instability.